COMP190 Digital Logic and Computer Design

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COMP190 Digital Logic and Computer Design

• Anselmo Lastra

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Todays Topics

• Course description
• Whats it about
• Mechanics grading, etc.
• Material from Chapter 1
• What is digital logic?
• Binary signaling
• Number systems
• Codes

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Whats Course About?

• Course will be COMP160
• Digital logic focusing on the design of computers
• Stay above transistor level
• Only one class on this
• Each person design a MIPS CPU
• And peripheral logic (VGA, keyboard)
• Mostly use high-level language
• Stay above gate level

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How Can We Do This?

• Field Programmable Gate Arrays
• Chips with a lot of circuits
• Tens of thousands to millions of transistors
• Programmable, either once or many times
• We write programs describing design
• Download to chip

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We Will Use This Board
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Schematic Diagram
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Verilog

• /
• A 32-bit counter with only 4 bits of output.
  The idea is
• to select which of the counter stages you
  want to pass on.
• Anselmo Lastra, November 2002
• /
• module cntr_32c(clk,res,out)
• input clk
• input res
• output 30 out
• reg 310 count
• always _at_ (posedge res or posedge clk)
• if(res)
• count
• else
• count

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Xylinx Software

• Use design tools from chip maker
• Have full version on lab PCs
• Webpack (version 6.1i) for your PC
• I can hand out CDs
• ModelSim simulator
• Full version in lab
• Can use free version on your PC, but slower

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Class Web Pages

• http//www.cs.unc.edu/lastra/comp190
• Lets browse
• Linked from my home page in case you forget
• All notes posted
• Will try to make put them there before class
• Blackboard for grades
• Class forum (linked to class page)
• Labs there also

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Textbook

• Morris Mano and Charles Kime
• Logic and Logic and Computer Design Fundamentals,
  3rd Edition
• Prentice Hall, 2004
• Will largely to follow text

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Overview of Textbook

• Chapters 1-6 Digital logic
• Combinational and sequential
• Chapter 7-8 Register Transfer and State Machines
• Chapter 9 Memories
• Chapters 10-12 Computer design
• Chapter 13 I/O
• Chapter 14 Memory Hierarchies

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Will Also Need

• COMP120 book
• For MIPS reference
• Verilog reference
• Book optional
• Web see course home page

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Grading

• Labs 35
• Easier at first latter ones will count more
• Homework 20
• Two tests spaced evenly 12.5 each
• Final 20

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Labs

• Paced slowly at first
• Familiarization with tools
• Build up computer components
• Registers, ALU, decoder
• Peripheral VGA, keyboard interface
• Assemble a simple MIPS
• Add more features
• Final demo game or similar

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Lab Sections

• Everyone signed up for 100 lab
• At limit of XSA cards
• Over number of computers
• Who will use laptop?
• No lab this Friday
• Begins next week

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Late Policy

• Homework assignments and lab reports due by class
  time (200 PM)
• One class late, 10 points off
• Two classes late, 25 points off
• Not accepted later

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Whats Your Background?

• Course experience
• Work, etc.
• Which COMP120?
• Whats your intent in taking class?
• Questions?

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Office Hours

• Would like to wait a week to set
• Or not have set hours
• Send email if you want to meet

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Now Shift to Technology

• Should be review

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Digital vs. Analog

• Analog infinite resolution
• Like (old fashioned) radio dial
• Digital a finite set of values
• Like money
• Cant get smaller than cents
• Typically also has maximum value

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Binary Signaling

• Zero volts
• FALSE or 0
• 3.3 or 5 volts
• TRUE or 1
• Why not multilevel signaling?

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Discrete Data

• Some data inherently discrete
• Names (sets of letters)
• Some quantized
• Music recorded from microphone
• Note that other examples like music from CD or
  electronic keyboard already quantized
• Mouse movement is quantized
• Well, some mouse movement

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Numbers and Arithmetic

• Review of binary numbers,
• Hexadecimal,
• Arithmetic,
• Other codes

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Binary Numbers

• Strings of binary digits (bits)
• One bit can store a number from 0 to 1
• n bits can store numbers from 0 to 2n

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Binary Powers of 2

• Positional representation
• Each digit represents a power of 2
• So 101 binary is
• 1 22 0 21 1 20
• or
• 1 4 0 2 1 1 5

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Converting Binary to Decimal

• Easy, just multiply digit by power of 2
• Just like a decimal number is represented
• Example follows

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Binary ? Decimal Example
What is 10011100 in decimal?
128 0 0 16 8 4 0 0
156
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Decimal to Binary

• A little more work than binary to decimal
• Some examples
• 3 2 1 11 (thats 121 120)
• 5 4 1 101 (thats 122 021 120)

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Algorithm Decimal to Binary

• Find largest power-of-two smaller than decimal
  number
• Make the appropriate binary digit a 1
• Subtract the power of 2 from decimal
• Do the same thing again

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Decimal ? Binary Example

• Convert 28 decimal to binary

32 is too large, so use 16
Binary ? 10000
Decimal ? 28 16 12
Next is 8
Binary ? 11000
Decimal ? 12 8 4
Next is 4
Binary ? 11100
Decimal ? 4 4 0
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Hexadecimal

• Strings of 0s and 1s too hard to write
• Use base-16 or hexadecimal 4 bits

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Hexadecimal

• Letters to represent 10-15

• Power of 2

• Size of byte

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Hex to Binary

• Convention write 0x before number
• Hex to Binary just convert digits

0x2ac
0x2ac 001010101100
No magic remember hex digit 4 bits
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Binary to Hex

• Just convert groups of 4 bits

101001101111011
1011
0101 ?
0111 ?
0011 ?
101001101111011 0x537b
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Hex to Decimal

• Just multiply each hex digit by decimal value,
  and add the results.

0x2ac
2 256
10 16
12 1
684
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Decimal to Hex

• Analogous to decimal ? binary.
• Find largest power-of-16 smaller than decimal
  number
• Divide by power-of-16. The integer result is hex
  digit.
• The remainder is new decimal number.
• Do the same thing again

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Decimal to Hex
684
0x2__
684/256 2
684256 172
0x2a_
172/16 10 a
0x2ac
17216 12 c
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Octal

• Octal is base 8
• Similar to hexadecimal
• Conversions
• Less convenient for use with 8-bit bytes

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BCD

• Binary Coded Decimal
• Decimal digits stored in binary
• Four bits/digit
• Like hex, except stops at 9
• Example
• 931 is coded as 1001 0011 0001
• Remember these are just encodings. Meanings are
  assigned by us.

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Other Codes Exist

• Non positional
• Example Gray Code
• Only one bit changes at a time
• 000,001,011,010,110,111,101,100
• Why is this useful?

Ref http//lib-www.lanl.gov/numerical/bookcpdf/c2
0-2.pdf
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Shaft Encoder
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Arithmetic -- addition

• Binary similar to decimal arithmetic

No carries
Carries
11 is 2 (or 102), which results in a carry
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Arithmetic -- subtraction
No borrows
Borrows
0 - 1 results in a borrow
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Arithmetic -- multiplication
Successive additions of multiplicand or
zero, multiplied by 2 (102). Note that
multiplication by 102 just shifts bits left.
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Hexadecimal Arithmetic

• Similar
• If youre doing by hand, easiest to convert each
  set of digits to decimal and back
• Skill is not very useful

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Character Codes

• From numbers to letters
• ASCII
• Stands for American Standard Code for Information
  Interchange
• Only 7 bits defined

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ASCII table
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Even Parity

• Sometimes high-order bit of ASCII coded to enable
  detection of errors
• Even parity set bit to make number of 1s even
• Examples
• A (01000001) with even parity is 01000001
• C (01000011) with even parity is 11000011

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Odd Parity

• Similar except make the number of 1s odd
• Examples
• A (01000001) with odd parity is 11000001
• C (01000011) with odd parity is 01000011

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Error Detection

• Note that parity detects only simple errors
• One, three, etc. bits
• More complex methods exist
• Some that enable recovery of original info
• Cost is more redundant bits

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Todays Topics

• Introduction
• Digital logic
• Number systems
• Arithmetic
• Codes
• Parity
• The encoding is key
• Standards are used to agree on encodings
• Special purpose codes for particular uses

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Homework

• None, but
• I expect you to be able to know binary number
  system and to do conversions
• Decimal Binary
• Binary Decimal
• Decimal Hex
• Hex Decimal
• Can do some of the problems 1-2, 1-4, 1-7.
  Answers on book website.

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Reading

• Skim chapter 1
• Quick read to make sure youre comfortable with
  material
• Read Chapter 2

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Next Week

• Combinational Logic Basics
• Lab preview
• Ill demo tools in class, probably Thursday
• Lab on Friday